Question

Find the centre and radius of each of the following circles.
(i) $x^2+y^2=25$
(ii) $(x-5{)}^2+(y-3{)}^2=20$
(iii) ${(x-\frac{1}{2})}^2+{(y+\frac{1}{3})}^2=\frac{1}{36}$

Answer 1

Equation of circle is given by:

$(x-a{)}^2+(y-b{)}^2=r^2$, where $(a,b)$ is the center and $r$ is the radius

(I) $x^2+y^2=25$

Center $=(0,0)$

Radius $=5$

(ii) $(x-5{)}^2+(y-3{)}^2=20$

Center $=(5,3)$

Radius $=\sqrt{20}=2\sqrt{5}$

(iii) ${(x-\frac{1}{2})}^2+{(y+\frac{1}{3})}^2=\frac{1}{36}$

Center $=(\frac{1}{2},\frac{-1}{3})$

Radius $=\frac{1}{6}$